Similar to Pierre's suggestion about not using soap to clean pots, you can make a pot scrubber by twisting a handful of green pine needles (dead brown ones work too, but aren't as tough) together, bend it in half, and you have a pretty good scrubber.

Once you've got the inside clean (enough), stick it back on the fire a second to dry and kill any possible bacteria. Wipe off the outside, and you're ready to toss it in the kitchen sack.